In Morris or song session I would not rule out others joining in verses either on tune (if same tune) or harmonies, or adding isntruments - even if in places they were countermelodies with meshing rhythms (so long as they were in tune and in time - someone knows who I am talking about.....). Since I usually accompanymyself on guitar there are often "bridge" sections on the guitar and I have been known to get very crabby when someone wants to play those differently, or press on into the next verse while I am still playing the "bridge".

BUT I do think it is bad form to sing different chorus or song words (except perhaps late in the evening when all have drink taken, and it makes more sense and fun say to sing a Kipper or other comedian version - eg "Rolling Drunk" in stead of "Rolling Home", although you have to pick your time and victim) or tunes unless they do harmonise.

Another thing I find very rude but sadly prevalent these days is that if say I start doing a song or have been doing a song, another person starts to sing it. Fine if I am not there, or if they have asked.   Again there are exceptions: when amongst good friends it can be a bit of fun to try to pre-empt someone by doing "his" song before him - and if the whole room does it it leaves him scratching for what to sing, grin, but again you have to pick your time and victim.